A359351 a(n) = A001952(A003151(n)).

6, 13, 23, 30, 40, 47, 54, 64, 71, 81, 88, 95, 105, 112, 122, 129, 139, 146, 153, 163, 170, 180, 187, 194, 204, 211, 221, 228, 238, 245, 252, 262, 269, 279, 286, 293, 303, 310, 320, 327, 334, 344, 351, 361, 368, 378, 385, 392, 402, 409, 419, 426, 433, 443

Offset: 1

Author

Clark Kimberling, Dec 27 2022

Keywords

• nonn
• easy

Comments

This is the third of four sequences that partition the positive integers. Starting with a general overview, suppose that u = (u(n)) and v = (v(n)) are increasing sequences of positive integers. For details, see A184922.

(1) u o v = (2, 5, 9, 12, 16, 19, 22, 26, 29, 33, 36, 39, 43, ...) = A184922

(2) u o v' = (1, 4, 7, 8, 11, 14, 15, 18, 21, 24, 25, 28, 31, ...) = A188376

(3) u' o v = (6, 13, 23, 30, 40, 47, 54, 64, 71, 81, 88, 95, ...) = A359351

(4) u' o v' = (3, 10, 17, 20, 27, 34, 37, 44, 51, 58, 61, 68, ...) = A188396

Crossrefs

Cf. A001951, A001952, A003151 (intersections instead of the rersults of composition), A003152, A184922, A188376, A356136, A188396, A341239 (results of reversed composition).

Programs

Mathematica

z = 1200; zz = 150;
u = Table[Floor[n Sqrt[2]], {n, 1, z}];
u1 = Complement[Range[Max[u]], u];
v = Table[Floor[n (1 + Sqrt[2])], {n, 1, z}];
v1 = Complement[Range[Max[v]], v];
Table[u[[v[[n]]]], {n, 1, zz}];   (* A184922 *)
Table[u[[v1[[n]]]], {n, 1, zz}];  (* A188376 *)
Table[u1[[v[[n]]]], {n, 1, zz}];  (* A359351 *)
Table[u1[[v1[[n]]]], {n, 1, zz}]; (* A188396 *)